Abstract: Lightning occurred in the atmosphere is a kind of long-distance discharge phenomenon, and it often causes a variety of disasters which become more serious by the extensive use of electronic devices particularly. With deep understanding on physical processes of lightning occurrence and development, lightning leader model is established based on observational facts to study development of lightning leader and its interaction with structures and provide reference for lightning protection. According to characteristics of CG lightning, a model of random lightning leader is established. The connection process of lightening leader is simulated. The model of lightning leader is developed by simulating ambient potential distribution using an over relaxation method. In the model, the direction of next leader step depends on the probability, and final connection location of downward leader is chosen randomly by the probability formula.The induced charge of downward leader increases with the propagation of downward leader. Simulation results of a random model show that the induced charge of downward leader is about 10^-4 C/m. With the development of the downward leader, the branch of downward leader increases. There are diversiform forms in connection process. Downward leader can connect with structure or ground which do not produce upward leader besides upward leader. Downward leader can connect with one of the upward leaders on the ground, and even connect with the ground which does not produce upward leader. Downward leader does not always connect with the tip of upward leader, and it can connect with one branch or middle of the upward leader. Lightning rod may do not produce upward leader and the downward leader above doesn't always connect with the lightning rod, sometimes it connects with structure and ground. The downward leader far away from lightning rod can also connect with the lightning rod. In most conditions, lightning rod can protect the structure from lightning. With fixed distances from downward leader and lightning rod, wider and lower structure is less likely protected by lightning rod.These simulation results are achieved with two-dimensional random lightning leader model within the range of limited space. More simulation and analysis are needed for three-dimensional random lightning leader model within larger spatial extent to find out the behavior characteristics of lightning rod and investigate the protection of lightning rod to buildings. A large number of natural lightning and triggered lightning observations are also needed to further check the reasonableness of the simulation results.